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3 years ago

What is the gcf of the numerator and denominator of the rational expression

Mathematics

1 answer:

Roman55 [17]3 years ago

5 0

$\frac{3x-15}{x^2-x-20} = \frac{3(x-5)}{(x+4)(x-5)}$

The only common factor is (x -5).

Selection A is appropriate.

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Step-by-step explanation:

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Calculus 3 chapter 16

o-na [289]

Evaluate $\vec F$ at $\vec r$ :

$\vec F(x,y,z) = x\,\vec\imath + y\,\vec\jmath + xy\,\vec k \\\\ \implies \vec F(\vec r(t)) = \vec F(\cos(t), \sin(t), t) = \cos(t)\,\vec\imath + \sin(t)\,\vec\jmath + \sin(t)\cos(t)\,\vec k$

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Simplifying the integrand, we have

$\vec F\cdot d\vec r = \bigg(-\cos(t)\sin(t) + \sin(t)\cos(t) + \sin(t)\cos(t)\bigg) \, dt \\ ~~~~~~~~= \sin(t)\cos(t) \, dt \\\\ ~~~~~~~~= \dfrac12 \sin(2t) \, dt$

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$\displaystyle \int_C \vec F\cdot d\vec r = \int_0^\pi \frac12\sin(2t)\,dt \\\\ ~~~~~~~~ = -\frac14\cos(2t) \bigg|_{t=0}^{t=\pi} \\\\ ~~~~~~~~ = -\frac14(\cos(2\pi)-\cos(0)) = \boxed{0}$

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2 years ago

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Step-by-step explanation:

Using the given function, we substitute c(x) = 114 and solve for x:

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24=12x

Divide both sides by 12:

2=x

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3 years ago

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